修饰主语的定语从句后的谓语用to do吗

定语从句没错,但是你划错范围了
从who一直到online都是修饰people的
所以句子的结构是people should be careful

这句话应该这样划分people (who use credit cardsto buy things online) should be careful ，所以主句是people should be careful，……的人应该要谨慎点。who use credit cardsto buy things online指在网上用信用卡购物的人。to buy是做use credit的补语。
判断定语从句，除了知道语法规则外，也要根据句子的意思来分析。所以要理解英语，语法和单词记忆是相辅相成的。

(who use credit cards to buy things online ）
这才是定语

拿掉就是people should be careful

括号内的是定语从句，但不完整，整个的定语从句应该是"who use credit cards to buy things online ",之所以是"to buy things"是因为前面有个"use",两个实义动词之间用"to"连接，即"use to buy".
over!!!